The term “vertical facelift” is one that is not clear. I would suggest to you that you find a surgeon who is experience with this surgery and can individualize the direction of pull to give you the result you seek.
There are many different types of facelift procedures. Some are simple while others are more complex. The goal of any facelift should be to leave the patient with a "balanced" youthful and rested appearance. Unfortunately "balanced" is a highly marketed catch word and may mean different things to different people. A "vertical" lift describes a direction of pull. It usually describes the direction of pull of the intermediate layers of tissue beneath the skin, often described as the "SMAS". You can think of it like a bed (the facial skeleton), the blankets (the SMAS) and the bedspread (the skin). The best facelifts lift the bedspread, tighten the blanket and the gently spread the bedspread back over the bed and blankets. Thus, the "tightening" of a facelift occurs beneath the skin. That way the skin is not "pulling" the rest of the face, which can give a pulled un-balanced appearance. When the SMAS is lift in a vertical direction it tends to give a more natural appearance.